\documentclass[tikz,border=2pt]{standalone}
\begin{document}

\begin{tikzpicture}
\draw[step=1,color=gray!40] (-2,-2) grid (2,2);
\draw[->] (-3,0) -- (3,0);
\draw[->] (0,-3) -- (0,3);
\draw[color=gray!40] (0,0) circle (1); %
\draw[color=red] (1,0) arc (0:45:1);
\draw[color=gray!40] (0,0) ellipse (1 and 0.5);
\draw[color=green] (1,0) arc (0:60:1 and 0.5);
\end{tikzpicture}

\end{document}